Testing for parameter constancy in GARCH(p,q) models

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Extensions of some classical methods in change point analysis (2014, methodology): “It is proven in Berkes et al. (2009b) that under assumption (8.”
Testing for a change in persistence in the presence of non-stationary volatility☆ (2008, methodology): “An alternative approach which we do not pursue in this paper, would be to assume a specific model for the volatility process and derive tests specifically for that model, as is done in the context of testing for change-points in GARCH processes by Berkes et al. (2004).”
Estimating Structural Changes in Regression Quantiles (2011, methodology): “Kokoszka and Leipus (1999, 2000) and Berkes et al. (2004) studied parameter change in GARCH processes.”
Recent Advances in ARCH Modelling (2007, methodology): “t=1 (Xt − EXt), τ ∈ [0, 1] } →D[0,1] {σW (τ), τ ∈ [0, 1]} , (15)”